docs: def dP_orifice(D, Do, P1, P2, C):
      r'''Calculates the non-recoverable pressure drop of an orifice plate based
      on the pressure drop and the geometry of the plate and the discharge 
      coefficient.
      
      .. math::
          \Delta\bar w = \frac{\sqrt{1-\beta^4(1-C^2)}-C\beta^2}
          {\sqrt{1-\beta^4(1-C^2)}+C\beta^2} (P_1 - P_2)
          
      Parameters
      ----------
      D : float
          Upstream internal pipe diameter, [m]
      Do : float
          Diameter of orifice at flow conditions, [m]
      P1 : float
          Static pressure of fluid upstream of orifice at the cross-section of
          the pressure tap, [Pa]
      P2 : float
          Static pressure of fluid downstream of orifice at the cross-section of
          the pressure tap, [Pa]
      C : float
          Coefficient of discharge of the orifice, [-]
  
      Returns
      -------
      dP : float
          Non-recoverable pressure drop of the orifice plate, [Pa]
  
      Notes
      -----
      This formula can be well approximated by:
          
      .. math::
          \Delta\bar w = \left(1 - \beta^{1.9}\right)(P_1 - P_2)
          
      The recoverable pressure drop should be recovered by 6 pipe diameters 
      downstream of the orifice plate.
      
      Examples
      --------
      >>> dP_orifice(D=0.07366, Do=0.05, P1=200000.0, P2=183000.0, C=0.61512)
      9069.474705745388
      
      References
      ----------
      .. [1] American Society of Mechanical Engineers. Mfc-3M-2004 Measurement 
         Of Fluid Flow In Pipes Using Orifice, Nozzle, And Venturi. ASME, 2001.
      .. [2] ISO 5167-2:2003 - Measurement of Fluid Flow by Means of Pressure 
         Differential Devices Inserted in Circular Cross-Section Conduits Running
         Full -- Part 2: Orifice Plates.
      '''
      beta = Do/D
      beta2 = beta*beta
      beta4 = beta2*beta2
      dP = P1 - P2
      delta_w = ((1.0 - beta4*(1.0 - C*C))**0.5 - C*beta2)/(
                 (1.0 - beta4*(1.0 - C*C))**0.5 + C*beta2)*dP
      return delta_w